Implementation with Evidence: Complete Information

We study full-implementation in Nash equilibrium under complete information. We generalize the canonical model (Maskin, 1977) by allowing agents to send evidence or discriminatory signals. A leading case is where evidence is hard information that proves something about the state of the world. In this environment, an implementable social choice rule need not be Maskin-monotonic. We formulate a weaker property, evidence-monotonicity, and show that this is a necessary condition for implementation. Evidence-monotonicity is also sufficient for implementation if there are three or more agents and the social choice rule satisfies two other properties—no veto power and non-satiation—that are reasonable in various settings, including “economic environments”. We discuss how natural conditions on the cost of discriminatory signals yield possibility results, in contrast with traditional negative results. Additional results are provided for the case of one and two agents.